Question

Suppose a \(100 \%\) sales tax is placed on a good. Explain with the use of graphs what will determine the incidence of that sales tax.

Short answer

To analyze the incidence of a 100% sales tax on a good, illustrate the initial supply and demand curves with price (P) and quantity (Q) axes. After introducing the sales tax, shift the supply curve vertically upwards by the initial price, and find the new equilibrium price (P2) and quantity (Q2) at the intersection of the demand curve and the new supply curve. The incidence of the sales tax depends on the relative price elasticities of supply and demand: if demand is more elastic, the burden falls primarily on sellers; if supply is more elastic, the burden falls primarily on buyers. The graph helps visualize the effects of the sales tax on market equilibrium and tax burden distribution.

Step-by-step solution

Illustrate the initial supply and demand curves

Begin by drawing a supply-demand graph with price (P) on the vertical axis and quantity (Q) on the horizontal axis. Draw the initial demand curve (D1) with a negative slope, reflecting the inverse relationship between price and quantity demanded, and the initial supply curve (S1) with a positive slope, illustrating the direct relationship between price and quantity supplied. At the intersection of both curves, we find the initial market equilibrium price (P1) and equilibrium quantity (Q1).

Introduce the sales tax

Now, introduce the 100% sales tax, which means that for every unit of the good sold, there will be an equal amount of tax paid. Since the tax is ultimately borne by the buyer, we can translate this tax into an increase in the price of the good. To include the sales tax in our graph, the supply curve has to be shifted vertically upward by the amount of the sales tax (equal to the initial price P1). Draw the new supply curve (S2) parallel to S1, at the level equal to P1 above the initial supply curve.

Find the new equilibrium price and quantity

Now that we have the new supply curve (S2) that considers the 100% sales tax, we can find the new market equilibrium price (P2) and equilibrium quantity (Q2). Locate the intersection of the demand curve (D1) and the new supply curve (S2). The price at this intersection point is the new equilibrium price (P2), and the corresponding quantity is the new equilibrium quantity (Q2).

Analyze the incidence of the sales tax

To determine the incidence of the sales tax, we need to analyze the burden distribution of the tax between the buyers and the sellers. The incidence of the sales tax depends on the relative price elasticities of supply and demand: - If the demand (buyers) is more price elastic than the supply (sellers), the sales tax burden falls primarily on the sellers. In this case, the new equilibrium price, P2, would be relatively lower than P1, as the buyers are more sensitive to price changes and the sellers have to pay more of the tax. - If the supply (sellers) is more price elastic than the demand (buyers), the sales tax burden falls primarily on the buyers. In this case, the new equilibrium price, P2, would be relatively higher than P1, as sellers are more sensitive to price changes and can pass most of the tax to the buyers. In conclusion, the incidence of a 100% sales tax depends on the relative price elasticities of supply and demand. The graph helps in visualizing how the sales tax affects the market equilibrium and the tax burden distribution between the buyers and the sellers.

Key concepts

Supply and Demand

Supply and demand are fundamental concepts in economics. They describe how prices and quantities of goods are determined in a market.
- **Demand** refers to the quantity of a good that consumers are willing and able to purchase at various prices. Typically, the demand curve slopes downward from left to right, illustrating that as prices drop, the quantity demanded increases.
- **Supply** refers to the quantity of a good that producers are willing and able to sell at various prices. The supply curve usually slopes upward, indicating that as prices rise, the quantity supplied also increases.
Market equilibrium occurs where the supply and demand curves intersect. This intersection determines the equilibrium price and quantity, where the quantity demanded equals the quantity supplied. Understanding these curves is crucial when analyzing how taxes affect market outcomes.

Elasticity

Elasticity measures how sensitive the quantity demanded or supplied is to changes in price. It plays a key role in determining tax incidence.
- **Price elasticity of demand** indicates how much the quantity demanded of a good changes in response to a change in price. When demand is elastic, consumers are sensitive to price changes; when it is inelastic, they are less sensitive.
- **Price elasticity of supply** shows how much the quantity supplied of a good changes in response to a change in price. Suppliers might be more or less willing to adjust the quantity they sell based on price changes.
The relative elasticity of demand and supply determines who will bear the brunt of a tax. If demand is more elastic than supply, sellers will incur more of the tax burden. Conversely, if supply is more elastic than demand, buyers will bear more of the burden. Therefore, knowing these elasticities helps predict how a tax affects prices and quantities, as well as how the burden is distributed.

Sales Tax

A sales tax is a tax imposed by the government on the sale of goods and services. It directly affects the supply curve in the market. With a 100% sales tax, for example, the cost of purchasing goods effectively doubles.
When such a tax is introduced, the supply curve shifts vertically upward by the tax amount. This represents the higher cost to consumers who now have to pay the price of the good plus the tax. The shift in the supply curve causes changes in the market equilibrium, leading to a new higher equilibrium price and typically a lower equilibrium quantity.
The incidence of the sales tax determines how much of the tax burden falls on sellers and how much on buyers. This distribution depends on the elasticities of supply and demand.

Market Equilibrium

Market equilibrium is the point where the quantity demanded equals the quantity supplied, resulting in an agreed-upon price and quantity in the market.
When a 100% sales tax is imposed, the market equilibrium is disturbed, leading to a new equilibrium. The new equilibrium price is higher because the supply curve shifts up by the tax amount. The overall quantity sold in the market typically decreases because the higher prices dissuade some buyers.
In analyzing market changes due to a tax, it's essential to consider the shifts in equilibrium. Equilibrium helps us understand the dynamics of how a tax influences market behavior, adjusting the prices paid and the quantities sold. In the new equilibrium, the actual burden of the tax on buyers and sellers can be determined by studying the shifts and the relative elasticity of demand and supply.